Full treatment of the proton radiography technique for laser-driven capacitor-coil targets

Ultrafast proton radiography has been frequently used for direct measurement of the electromagnetic fields around laser-driven capacitor-coil targets. The goal is to accurately infer the coil currents and their magnetic field generation for a robust magnetic field source that can lead to many applications. The technique often involves numerical calculations for synthetic proton images to reproduce experimental measurements. While electromagnetic fields are the primary source for proton deflections around the capacitor coils, stopping power and small angle deflection can also contribute to the observed experimental features. Here we present a comprehensive study of the proton radiography technique including all sources of proton deflections as a function of coil shapes, current magnitudes, and proton energies. Good agreements were achieved between experimental data and numerical calculations that include both the stopping power and small angle deflections, particularly when the induced coil currents were small.